Assessing the numerical dissipation rate and viscosity in numerical simulations of fluid flows

A numerical dissipation rate and viscosity in flow simulations with realistic geometry using low-order compressible Navier–Stokes solvers

“…To date the methodology proposed by Schranner et al (2015) has been applied only to a Taylor-Green vortex flow which is a flow that evolves in a box with periodic boundary conditions. In order to both confirm that the higher viscous dissipation is effectively coming from the shear layer and to investigate the effects of the presence of a no-slip boundary condition, another set of three sub-domains have been analyzed with approximatively the same sub-domain volumes.…”

“…13have been calculated on-the-fly using the post-processing capabilities of the code itself. We can rely on the low-order post-processing tools embedded in the software since Schranner et al (2015) showed that even with a loworder reconstruction one can obtain fair estimates of the terms in the kinetic energy balance. For the time discretization a second-order three-points finite difference formula is used, i.e.…”

“…where ∆V (m) is the volume of the m th control volume. These steps have been previously validated for Star-CCM+ by repeating the same test cases as in Schranner et al (2015) for both incompressible and compressible solvers (Castiglioni and Domaradzki, 2015). Even though in this study a specific commercial software has been used, it is important to stress that the solver is treated as a black box and that all that is required to perform this analysis are temporal snapshots of the flow fields.…”

“…In the above equation the subscript [ ] (m) refers to the m th control volume. We call the residual ε n the numerical dissipation rate because it has been shown that if integrated over a sufficiently large control volume it has a predominantly dissipative character (Schranner et al, 2015;Domaradzki and Radhakrishnan, 2005). Eq.…”

“…The dissipation energy is then estimated by computing the energy flux at the resolved energy containing scales which are not influenced by the specifics of the numerical scheme. The need to assess the numerical dissipation in non-periodic domains has been addressed by Schranner et al (2015). Following the work of Domaradzki et al (2003); Domaradzki and Radhakrishnan (2005), Schranner et al (2015) developed a methodology that allows for the quantification of the numerical dissipation for an arbitrary CFD code in a self consistent way, i.e., using only information about the flow field provided by the code being analyzed, viz., the solver can be treated as a black box without the need to know the details of the implementation.…”